The objective of this paper is to study the mean–variance portfolio
optimization in continuous time. Since this problem is time inconsistent
we attack it by placing the problem within a game theoretic framework
and look for subgame perfect Nash equilibrium strategies. This particular
problem has already been studied in [2] where the authors assumed a con-
stant risk aversion parameter. This assumption leads to an equilibrium
control where the dollar amount invested in the risky asset is independent
of current wealth, and we argue that this result is unrealistic from an eco-
nomic point of view. In order to have a more realistic model we instead
study the case when the risk aversion depends dynamically on current
wealth. This is a substantially more complicated problem than the one
with constant risk aversion but, using the general theory of time inconsis-
tent control developed in [4], we provide a fairly detailed analysis on the
general case. In particular, when the risk aversion is inversely proportional
to wealth, we provide an analytical solution where the equilibrium dollar
amount invested in the risky asset is proportional to current wealth. The
equilibrium for this model thus appears more reasonable than the one for
the model with constant risk aversion.

We investigate the possibility of an arbitrage free model for the term structure of interest rates where the yield curve only changes through a parallel shift. We consider HJM type forward rate models driven by a multidimensionalWiener process as well as by a general marked point process. Within this general framework we show that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. We also show that there exists no nontrivial flat term structure model. The same analysis is repeated for the similar case, where the yield curve only changes through proportional shifts.
Key words: bond market, term structure of interest rates, flat term structures.